Question

A fluid flows though a horizontal 0.1 inch diameter pipe. When the Reynold number is 1508, the head loss over a 20-ft length of the pipe is 6.2 ft. Determine the fluid velocity.

Answer 1

The fluid velocity V = 1.98 ft/s

Step-by-step explanation:

From the information given:

The fluid velocity can be determined from the head-loss
`h_L` of a laminar pipe and it is expressed as:

`h_L = f(l* V^2)/(D * 2g)`

where;

f = frictional factor ; l = length; D = diameter; V= fluid velocity and g = acceleration due to gravity.

And;

`f = (64)/(Re)`

For fluid movement in a laminar flow, the Reynolds number (Re) is usually lesser than 2100.

Given that:

Re = 1508 < 2100 ( laminar flow)

Then;

`f = (64)/(1508)`

f = 0.04244

Also;

the head-loss
`h_L` = 6.2 ft

frictional force f = 0.04244

length = 20-ft

acceleration due to gravity (g) = 32.2 ft/s²

Replacing all the values into the equation
`h_L = f(l* V^2)/(D * 2g)`; the fluid velocity is:

`6.2 = 0.04244 * (20 * V^2)/(0.1 * (1)/(12) * 2* 32.2)`

`6.2 = 0.04244 * (20 * V^2)/(0.53667)`

6.2 × 0.53667 = 0.04244 × 20 × V²

3.327354 = 0.8488 × V²

`V^2= \frac{3.327354} { 0.8488}`

`V^2=3.92`

`V = √(3.92)`

V = 1.98 ft/s